Theorems · Theorem · logic and foundations
Set.countable_infinite_iff_nonempty_denumerable
∀ {α : Type u_1} {s : Set α}, s.Countable ∧ s.Infinite ↔ Nonempty (Denumerable ↑s)- Defined in
- Mathlib.SetTheory.Cardinal.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemstatement and proof · cited by 7,166
- Countableproof · cited by 633
- Set.Countablestatement and proof · cited by 545
- Infiniteproof · cited by 352
- Set.Infinitestatement and proof · cited by 263
- Denumerablestatement · cited by 28
- Set.infinite_coe_iffproof · cited by 16
- Set.countable_coe_iffproof · cited by 15
- nonempty_denumerable_iffproof · cited by 1
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